Subgroups — C₁₃₇×#20018 #46869404

Order 35072.

604 conjugacy classes of subgroups.

The subgroup lattice has 396 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#3396×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
2	#3394×C₁₃₇	C₂	1	2	yes	maximal, complemented
3	#3342×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
4	#1706×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
5	#1674×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
6	#1667×C₁₃₇	C₂	1	1	yes	maximal, characteristic
7	#1666×C₁₃₇	C₂	1	2	yes	maximal, complemented
8	#1640×C₁₃₇	C₂	1	2	yes	maximal, complemented
9	#1628×C₁₃₇	C₂	1	2	yes	maximal, complemented
10	C₈×Q₁₆×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
11	C₈×SD₁₆×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
12	#559×C₁₃₇	C₂²	1	2	yes	—
13	#556×C₁₃₇	C₂²	1	2	yes	—
14	#500×C₁₃₇	C₂²	1	1	yes	characteristic
15	#495×C₁₃₇	—	2	1	no	—
16	#495×C₁₃₇	—	2	2	no	—
17	#493×C₁₃₇	C₂²	1	1	yes	characteristic
18	#492×C₁₃₇	C₂²	1	2	yes	—
19	#486×C₁₃₇	C₂²	1	2	yes	—
20	#485×C₁₃₇	—	2	2	no	—
21	#475×C₁₃₇	C₂²	1	2	yes	—
22	#467×C₁₃₇	—	2	1	no	—
23	#464×C₁₃₇	—	2	2	no	—
24	#463×C₁₃₇	—	2	2	no	—
25	#463×C₁₃₇	—	2	2	no	—
26	#462×C₁₃₇	C₂²	1	2	yes	—
27	#460×C₁₃₇	C₂²	1	2	yes	—
28	#459×C₁₃₇	C₂²	1	2	yes	—
29	C₈×Q₈×C₁₃₇	C₂²	1	1	yes	characteristic
30	C₈×Q₈×C₁₃₇	C₂²	1	2	yes	—
31	C₄×Q₁₆×C₁₃₇	C₂²	1	1	yes	characteristic
32	C₄×SD₁₆×C₁₃₇	—	2	2	no	—
33	C₄×SD₁₆×C₁₃₇	C₂²	1	1	yes	characteristic
34	C₄×D₈×C₁₃₇	—	2	1	no	—
35	C₈×D₄×C₁₃₇	C₂²	1	1	yes	characteristic
36	#427×C₁₃₇	—	2	1	no	—
37	#335×C₁₃₇	C₂²	1	1	yes	characteristic
38	#334×C₁₃₇	C₂²	1	1	yes	characteristic
39	#332×C₁₃₇	C₂²	1	2	yes	—
40	#331×C₁₃₇	C₂²	1	2	yes	—
41	Q₈⋊C₈×C₁₃₇	C₂²	1	1	yes	characteristic
42	Q₈⋊C₈×C₁₃₇	C₂²	1	2	yes	—
43	D₄⋊C₈×C₁₃₇	C₂²	1	1	yes	characteristic
44	C₈²×C₁₃₇	C₂²	1	1	yes	characteristic
45	C₂×Q₁₆×C₁₃₇	—	2	2	no	—
46	C₂×Q₁₆×C₁₃₇	D₄	1	1	yes	characteristic
47	C₂×SD₁₆×C₁₃₇	—	2	2	no	—
48	C₂×SD₁₆×C₁₃₇	—	2	2	no	—
49	C₂×SD₁₆×C₁₃₇	—	2	2	no	—
50	C₂×SD₁₆×C₁₃₇	D₄	1	1	yes	characteristic
51	C₂×D₈×C₁₃₇	—	2	2	no	—
52	C₂×D₈×C₁₃₇	—	2	1	no	—
53	C₂×D₈×C₁₃₇	—	2	1	no	—
54	C₂²×C₈×C₁₃₇	—	2	1	no	—
55	C₄⋊Q₈×C₁₃₇	C₂³	1	2	yes	—
56	#127×C₁₃₇	C₂³	1	2	yes	—
57	#126×C₁₃₇	—	4	2	no	—
58	#124×C₁₃₇	—	2	2	no	—
59	#124×C₁₃₇	—	2	2	no	—
60	#124×C₁₃₇	—	2	2	no	—
61	#123×C₁₃₇	—	4	2	no	—
62	C₂²⋊Q₈×C₁₃₇	—	2	2	no	—
63	C₄×Q₈×C₁₃₇	—	2	2	no	—
64	C₄×Q₈×C₁₃₇	C₂³	1	1	yes	characteristic
65	C₄×Q₈×C₁₃₇	C₂³	1	2	yes	—
66	C₄×D₄×C₁₃₇	—	2	2	no	—
67	C₄×D₄×C₁₃₇	—	2	2	no	—
68	C₄×D₄×C₁₃₇	C₂³	1	1	yes	characteristic
69	#117×C₁₃₇	—	2	2	no	—
70	#107×C₁₃₇	—	2	1	no	—
71	#107×C₁₃₇	—	2	1	no	—
72	#107×C₁₃₇	D₄	1	1	yes	characteristic
73	#106×C₁₃₇	—	2	2	no	—
74	#106×C₁₃₇	D₄	1	1	yes	characteristic
75	C₄⋊C₈×C₁₃₇	—	2	1	no	—
76	C₄⋊C₈×C₁₃₇	—	2	2	no	—
77	C₄⋊C₈×C₁₃₇	C₂³	1	1	yes	characteristic
78	C₄⋊C₈×C₁₃₇	C₂³	1	2	yes	—
79	C₄⋊C₈×C₁₃₇	C₂³	1	1	yes	characteristic
80	#103×C₁₃₇	—	2	2	no	—
81	#103×C₁₃₇	—	2	2	no	—
82	#103×C₁₃₇	D₄	1	1	yes	characteristic
83	#103×C₁₃₇	D₄	1	2	yes	—
84	#102×C₁₃₇	—	2	2	no	—
85	#102×C₁₃₇	—	2	2	no	—
86	#102×C₁₃₇	—	4	2	no	—
87	#102×C₁₃₇	D₄	1	1	yes	characteristic
88	C₂²⋊C₈×C₁₃₇	—	2	1	no	—
89	C₄×C₈×C₁₃₇	—	2	1	no	—
90	C₄×C₈×C₁₃₇	—	2	2	no	—
91	C₄×C₈×C₁₃₇	C₂³	1	1	yes	characteristic
92	C₄×C₈×C₁₃₇	C₂³	1	1	yes	characteristic
93	C₄×C₈×C₁₃₇	C₂³	1	1	yes	characteristic
94	C₂×Q₈×C₁₃₇	—	2	2	no	—
95	C₂×Q₈×C₁₃₇	C₂×D₄	1	2	yes	—
96	C₂×Q₈×C₁₃₇	C₂×D₄	1	1	yes	characteristic
97	C₂×D₄×C₁₃₇	—	2	2	no	—
98	C₂×D₄×C₁₃₇	—	2	2	no	—
99	C₂×D₄×C₁₃₇	—	2	2	no	—
100	C₂×D₄×C₁₃₇	C₂×D₄	1	1	yes	characteristic
101	C₂²×C₄×C₁₃₇	—	2	1	no	—
102	C₂²×C₄×C₁₃₇	—	4	2	no	—
103	Q₁₆×C₁₃₇	—	2	2	no	—
104	Q₁₆×C₁₃₇	—	8	2	no	—
105	SD₁₆×C₁₃₇	—	2	2	no	—
106	SD₁₆×C₁₃₇	—	4	4	no	—
107	SD₁₆×C₁₃₇	—	8	2	no	—
108	SD₁₆×C₁₃₇	—	8	2	no	—
109	D₈×C₁₃₇	—	4	2	no	—
110	D₈×C₁₃₇	—	8	1	no	—
111	D₈×C₁₃₇	—	8	2	no	—
112	C₂×C₈×C₁₃₇	—	2	1	no	—
113	C₂×C₈×C₁₃₇	—	2	2	no	—
114	C₂×C₈×C₁₃₇	—	2	1	no	—
115	C₂×C₈×C₁₃₇	—	2	1	no	—
116	C₂×C₈×C₁₃₇	—	4	2	no	—
117	C₂×C₈×C₁₃₇	C₂×D₄	1	1	yes	characteristic
118	C₂×C₈×C₁₃₇	C₂×D₄	1	1	yes	characteristic
119	C₂×C₈×C₁₃₇	C₂×D₄	1	1	yes	characteristic
120	C₂×C₈×C₁₃₇	C₂×D₄	1	1	yes	characteristic
121	C₄⋊C₄×C₁₃₇	—	2	1	no	—
122	C₄⋊C₄×C₁₃₇	—	2	2	no	—
123	C₄⋊C₄×C₁₃₇	—	2	2	no	—
124	C₄⋊C₄×C₁₃₇	—	2	2	no	—
125	C₄⋊C₄×C₁₃₇	—	4	2	no	—
126	C₄⋊C₄×C₁₃₇	C₂×D₄	1	1	yes	characteristic
127	C₄⋊C₄×C₁₃₇	C₂×D₄	1	2	yes	—
128	C₄⋊C₄×C₁₃₇	C₂×D₄	1	1	yes	characteristic
129	C₂²⋊C₄×C₁₃₇	—	2	1	no	—
130	C₂²⋊C₄×C₁₃₇	—	4	2	no	—
131	C₂²⋊C₄×C₁₃₇	—	4	2	no	—
132	C₂²⋊C₄×C₁₃₇	—	4	2	no	—
133	C₂²⋊C₄×C₁₃₇	—	4	2	no	—
134	C₂²⋊C₄×C₁₃₇	—	4	2	no	—
135	C₄²×C₁₃₇	—	2	1	no	—
136	C₄²×C₁₃₇	—	2	2	no	—
137	C₄²×C₁₃₇	—	4	2	no	—
138	C₄²×C₁₃₇	C₂⁴	1	1	yes	characteristic
139	C₂³×C₁₃₇	—	2	1	no	—
140	C₂³×C₁₃₇	—	4	2	no	—
141	Q₈×C₁₃₇	—	2	1	no	—
142	Q₈×C₁₃₇	—	2	2	no	—
143	Q₈×C₁₃₇	—	2	1	no	—
144	Q₈×C₁₃₇	—	2	2	no	—
145	Q₈×C₁₃₇	—	4	2	no	—
146	Q₈×C₁₃₇	—	4	2	no	—
147	D₄×C₁₃₇	—	2	1	no	—
148	D₄×C₁₃₇	—	2	1	no	—
149	D₄×C₁₃₇	—	4	2	no	—
150	D₄×C₁₃₇	—	4	2	no	—
151	D₄×C₁₃₇	—	4	2	no	—
152	D₄×C₁₃₇	—	4	2	no	—
153	D₄×C₁₃₇	—	8	2	no	—
154	C₂×C₄×C₁₃₇	—	2	2	no	—
155	C₂×C₄×C₁₃₇	—	2	1	no	—
156	C₂×C₄×C₁₃₇	—	2	2	no	—
157	C₂×C₄×C₁₃₇	—	2	1	no	—
158	C₂×C₄×C₁₃₇	—	2	1	no	—
159	C₂×C₄×C₁₃₇	—	4	1	no	—
160	C₂×C₄×C₁₃₇	—	4	1	no	—
161	C₂×C₄×C₁₃₇	—	4	2	no	—
162	C₂×C₄×C₁₃₇	—	16	2	no	—
163	C₂×C₄×C₁₃₇	C₂²×D₄	1	1	yes	characteristic
164	C₂×C₄×C₁₃₇	C₂²×D₄	1	1	yes	characteristic
165	C₂×C₄×C₁₃₇	H(5,𝔽₂)	1	1	yes	characteristic
166	C₈×C₁₃₇	—	2	1	no	—
167	C₈×C₁₃₇	—	2	1	no	—
168	C₈×C₁₃₇	—	4	1	no	—
169	C₈×C₁₃₇	—	4	1	no	—
170	C₈×C₁₃₇	—	4	2	no	—
171	C₈×C₁₃₇	—	4	1	no	—
172	C₈×C₁₃₇	#135	1	2	yes	—
173	C₈×C₁₃₇	#135	1	2	yes	—
174	C₂²×C₁₃₇	—	4	1	no	—
175	C₂²×C₁₃₇	—	4	1	no	—
176	C₂²×C₁₃₇	—	4	1	no	—
177	C₂²×C₁₃₇	—	8	2	no	—
178	C₂²×C₁₃₇	—	8	2	no	—
179	C₂²×C₁₃₇	—	8	2	no	—
180	C₂²×C₁₃₇	D₄²	1	1	yes	characteristic
181	C₄×C₁₃₇	—	2	1	no	—
182	C₄×C₁₃₇	—	4	1	no	—
183	C₄×C₁₃₇	—	4	2	no	—
184	C₄×C₁₃₇	—	4	1	no	—
185	C₄×C₁₃₇	—	4	2	no	—
186	C₄×C₁₃₇	—	4	1	no	—
187	C₄×C₁₃₇	—	8	2	no	—
188	C₄×C₁₃₇	C₂×#135	1	1	yes	characteristic
189	C₄×C₁₃₇	C₂×#135	1	1	yes	characteristic
190	C₄×C₁₃₇	#576	1	1	yes	characteristic
191	C₄×C₁₃₇	#577	1	1	yes	characteristic
192	C₂×C₁₃₇	—	8	1	no	—
193	C₂×C₁₃₇	—	16	2	no	—
194	C₂×C₁₃₇	#3284	1	1	yes	characteristic
195	C₂×C₁₃₇	#3287	1	1	yes	characteristic
196	C₂×C₁₃₇	#3290	1	1	yes	characteristic
197	#20018	C₁₃₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
198	C₁₃₇	#20018	1	1	yes	characteristic, direct product factor, Sylow
199	#3396	C₂×C₁₃₇	1	1	yes	characteristic, complemented
200	#3394	C₂×C₁₃₇	1	2	yes	complemented
201	#3342	C₂×C₁₃₇	1	1	yes	characteristic, complemented
202	#1706	C₂×C₁₃₇	1	1	yes	characteristic, complemented
203	#1674	C₂×C₁₃₇	1	1	yes	characteristic, complemented
204	#1667	C₂×C₁₃₇	1	1	yes	characteristic
205	#1666	C₂×C₁₃₇	1	2	yes	complemented
206	#1640	C₂×C₁₃₇	1	2	yes	complemented
207	#1628	C₂×C₁₃₇	1	2	yes	complemented
208	C₈×Q₁₆	C₂×C₁₃₇	1	1	yes	characteristic, complemented
209	C₈×SD₁₆	C₂×C₁₃₇	1	1	yes	characteristic, complemented
210	#559	C₂²×C₁₃₇	1	2	yes	—
211	#556	C₂²×C₁₃₇	1	2	yes	—
212	#500	C₂²×C₁₃₇	1	1	yes	characteristic
213	#495	—	2	1	no	—
214	#495	—	2	2	no	—
215	#493	C₂²×C₁₃₇	1	1	yes	characteristic
216	#492	C₂²×C₁₃₇	1	2	yes	—
217	#486	C₂²×C₁₃₇	1	2	yes	—
218	#485	—	2	2	no	—
219	#475	C₂²×C₁₃₇	1	2	yes	—
220	#467	—	2	1	no	—
221	#464	—	2	2	no	—
222	#463	—	2	2	no	—
223	#463	—	2	2	no	—
224	#462	C₂²×C₁₃₇	1	2	yes	—
225	#460	C₂²×C₁₃₇	1	2	yes	—
226	#459	C₂²×C₁₃₇	1	2	yes	—
227	C₈×Q₈	C₂²×C₁₃₇	1	1	yes	characteristic
228	C₈×Q₈	C₂²×C₁₃₇	1	2	yes	—
229	C₄×Q₁₆	C₂²×C₁₃₇	1	1	yes	characteristic
230	C₄×SD₁₆	—	2	2	no	—
231	C₄×SD₁₆	C₂²×C₁₃₇	1	1	yes	characteristic
232	C₄×D₈	—	2	1	no	—
233	C₈×D₄	C₂²×C₁₃₇	1	1	yes	characteristic
234	#427	—	2	1	no	—
235	#335	C₂²×C₁₃₇	1	1	yes	characteristic
236	#334	C₂²×C₁₃₇	1	1	yes	characteristic
237	#332	C₂²×C₁₃₇	1	2	yes	—
238	#331	C₂²×C₁₃₇	1	2	yes	—
239	Q₈⋊C₈	C₂²×C₁₃₇	1	1	yes	characteristic
240	Q₈⋊C₈	C₂²×C₁₃₇	1	2	yes	—
241	D₄⋊C₈	C₂²×C₁₃₇	1	1	yes	characteristic
242	C₈²	C₂²×C₁₃₇	1	1	yes	characteristic
243	C₂×Q₁₆	—	2	2	no	—
244	C₂×Q₁₆	D₄×C₁₃₇	1	1	yes	characteristic
245	C₂×SD₁₆	—	2	2	no	—
246	C₂×SD₁₆	—	2	2	no	—
247	C₂×SD₁₆	—	2	2	no	—
248	C₂×SD₁₆	D₄×C₁₃₇	1	1	yes	characteristic
249	C₂×D₈	—	2	2	no	—
250	C₂×D₈	—	2	1	no	—
251	C₂×D₈	—	2	1	no	—
252	C₂²×C₈	—	2	1	no	—
253	C₄⋊Q₈	C₂³×C₁₃₇	1	2	yes	—
254	#127	C₂³×C₁₃₇	1	2	yes	—
255	#126	—	4	2	no	—
256	#124	—	2	2	no	—
257	#124	—	2	2	no	—
258	#124	—	2	2	no	—
259	#123	—	4	2	no	—
260	C₂²⋊Q₈	—	2	2	no	—
261	C₄×Q₈	—	2	2	no	—
262	C₄×Q₈	C₂³×C₁₃₇	1	2	yes	—
263	C₄×Q₈	C₂³×C₁₃₇	1	1	yes	characteristic
264	C₄×D₄	—	2	2	no	—
265	C₄×D₄	—	2	2	no	—
266	C₄×D₄	C₂³×C₁₃₇	1	1	yes	characteristic
267	#117	—	2	2	no	—
268	#107	—	2	1	no	—
269	#107	—	2	1	no	—
270	#107	D₄×C₁₃₇	1	1	yes	characteristic
271	#106	—	2	2	no	—
272	#106	D₄×C₁₃₇	1	1	yes	characteristic
273	C₄⋊C₈	—	2	1	no	—
274	C₄⋊C₈	—	2	2	no	—
275	C₄⋊C₈	C₂³×C₁₃₇	1	1	yes	characteristic
276	C₄⋊C₈	C₂³×C₁₃₇	1	1	yes	characteristic
277	C₄⋊C₈	C₂³×C₁₃₇	1	2	yes	—
278	#103	—	2	2	no	—
279	#103	—	2	2	no	—
280	#103	D₄×C₁₃₇	1	1	yes	characteristic
281	#103	D₄×C₁₃₇	1	2	yes	—
282	#102	—	2	2	no	—
283	#102	—	2	2	no	—
284	#102	—	4	2	no	—
285	#102	D₄×C₁₃₇	1	1	yes	characteristic
286	C₂²⋊C₈	—	2	1	no	—
287	C₄×C₈	—	2	1	no	—
288	C₄×C₈	—	2	2	no	—
289	C₄×C₈	C₂³×C₁₃₇	1	1	yes	characteristic
290	C₄×C₈	C₂³×C₁₃₇	1	1	yes	characteristic
291	C₄×C₈	C₂³×C₁₃₇	1	1	yes	characteristic
292	C₂×Q₈	—	2	2	no	—
293	C₂×Q₈	C₂×D₄×C₁₃₇	1	2	yes	—
294	C₂×Q₈	C₂×D₄×C₁₃₇	1	1	yes	characteristic
295	C₂×D₄	—	2	2	no	—
296	C₂×D₄	—	2	2	no	—
297	C₂×D₄	—	2	2	no	—
298	C₂×D₄	C₂×D₄×C₁₃₇	1	1	yes	characteristic
299	C₂²×C₄	—	2	1	no	—
300	C₂²×C₄	—	4	2	no	—
301	Q₁₆	—	2	2	no	—
302	Q₁₆	—	8	2	no	—
303	SD₁₆	—	2	2	no	—
304	SD₁₆	—	4	4	no	—
305	SD₁₆	—	8	2	no	—
306	SD₁₆	—	8	2	no	—
307	D₈	—	4	2	no	—
308	D₈	—	8	1	no	—
309	D₈	—	8	2	no	—
310	C₂×C₈	—	2	1	no	—
311	C₂×C₈	—	2	2	no	—
312	C₂×C₈	—	2	1	no	—
313	C₂×C₈	—	2	1	no	—
314	C₂×C₈	—	4	2	no	—
315	C₂×C₈	C₂×D₄×C₁₃₇	1	1	yes	characteristic
316	C₂×C₈	C₂×D₄×C₁₃₇	1	1	yes	characteristic
317	C₂×C₈	C₂×D₄×C₁₃₇	1	1	yes	characteristic
318	C₂×C₈	C₂×D₄×C₁₃₇	1	1	yes	characteristic
319	C₄⋊C₄	—	2	1	no	—
320	C₄⋊C₄	—	2	2	no	—
321	C₄⋊C₄	—	2	2	no	—
322	C₄⋊C₄	—	2	2	no	—
323	C₄⋊C₄	—	4	2	no	—
324	C₄⋊C₄	C₂×D₄×C₁₃₇	1	1	yes	characteristic
325	C₄⋊C₄	C₂×D₄×C₁₃₇	1	2	yes	—
326	C₄⋊C₄	C₂×D₄×C₁₃₇	1	1	yes	characteristic
327	C₂²⋊C₄	—	2	1	no	—
328	C₂²⋊C₄	—	4	2	no	—
329	C₂²⋊C₄	—	4	2	no	—
330	C₂²⋊C₄	—	4	2	no	—
331	C₂²⋊C₄	—	4	2	no	—
332	C₂²⋊C₄	—	4	2	no	—
333	C₄²	—	2	1	no	—
334	C₄²	—	2	2	no	—
335	C₄²	—	4	2	no	—
336	C₄²	C₂⁴×C₁₃₇	1	1	yes	characteristic
337	C₂³	—	2	1	no	—
338	C₂³	—	4	2	no	—
339	Q₈	—	2	1	no	—
340	Q₈	—	2	2	no	—
341	Q₈	—	2	1	no	—
342	Q₈	—	2	2	no	—
343	Q₈	—	4	2	no	—
344	Q₈	—	4	2	no	—
345	D₄	—	2	1	no	—
346	D₄	—	2	1	no	—
347	D₄	—	4	2	no	—
348	D₄	—	4	2	no	—
349	D₄	—	4	2	no	—
350	D₄	—	4	2	no	—
351	D₄	—	8	2	no	—
352	C₂×C₄	—	2	2	no	—
353	C₂×C₄	—	2	1	no	—
354	C₂×C₄	—	2	2	no	—
355	C₂×C₄	—	2	1	no	—
356	C₂×C₄	—	2	1	no	—
357	C₂×C₄	—	4	1	no	—
358	C₂×C₄	—	4	1	no	—
359	C₂×C₄	—	4	2	no	—
360	C₂×C₄	—	16	2	no	—
361	C₂×C₄	C₂²×D₄×C₁₃₇	1	1	yes	characteristic
362	C₂×C₄	C₂²×D₄×C₁₃₇	1	1	yes	characteristic
363	C₂×C₄	H(5,𝔽₂)×C₁₃₇	1	1	yes	characteristic
364	C₈	—	2	1	no	—
365	C₈	—	2	1	no	—
366	C₈	—	4	1	no	—
367	C₈	—	4	1	no	—
368	C₈	—	4	2	no	—
369	C₈	—	4	1	no	—
370	C₈	#135×C₁₃₇	1	2	yes	—
371	C₈	#135×C₁₃₇	1	2	yes	—
372	C₂²	—	4	1	no	—
373	C₂²	—	4	1	no	—
374	C₂²	—	4	1	no	—
375	C₂²	—	8	2	no	—
376	C₂²	—	8	2	no	—
377	C₂²	—	8	2	no	—
378	C₂²	D₄²×C₁₃₇	1	1	yes	characteristic
379	C₄	—	2	1	no	—
380	C₄	—	4	1	no	—
381	C₄	—	4	2	no	—
382	C₄	—	4	1	no	—
383	C₄	—	4	1	no	—
384	C₄	—	4	2	no	—
385	C₄	—	8	2	no	—
386	C₄	C₂×#135×C₁₃₇	1	1	yes	characteristic
387	C₄	C₂×#135×C₁₃₇	1	1	yes	characteristic
388	C₄	#576×C₁₃₇	1	1	yes	characteristic
389	C₄	#577×C₁₃₇	1	1	yes	characteristic
390	C₂	—	8	1	no	—
391	C₂	—	16	2	no	—
392	C₂	#3284×C₁₃₇	1	1	yes	characteristic
393	C₂	#3287×C₁₃₇	1	1	yes	characteristic
394	C₂	#3290×C₁₃₇	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₃₇	D₄²
commutator, Frattini, cosocle	C₄²	C₂⁴×C₁₃₇
prime radical	#1667×C₁₃₇	C₂
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃₇ ◁ C₄²×C₁₃₇ ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
1. #3396×C₁₃₇	C₂	semidirect
2. #3394×C₁₃₇	C₂	semidirect
3. #3342×C₁₃₇	C₂	semidirect
4. #1706×C₁₃₇	C₂	semidirect
5. #1674×C₁₃₇	C₂	semidirect
7. #1666×C₁₃₇	C₂	semidirect
8. #1640×C₁₃₇	C₂	semidirect
9. #1628×C₁₃₇	C₂	semidirect
10. C₈×Q₁₆×C₁₃₇	C₂	semidirect
11. C₈×SD₁₆×C₁₃₇	C₂	semidirect
197. #20018	C₁₃₇	direct (N × H)
198. C₁₃₇	#20018	direct (N × H)
199. #3396	C₂×C₁₃₇	semidirect
200. #3394	C₂×C₁₃₇	semidirect
201. #3342	C₂×C₁₃₇	semidirect
202. #1706	C₂×C₁₃₇	semidirect
203. #1674	C₂×C₁₃₇	semidirect
205. #1666	C₂×C₁₃₇	semidirect
206. #1640	C₂×C₁₃₇	semidirect
207. #1628	C₂×C₁₃₇	semidirect
208. C₈×Q₁₆	C₂×C₁₃₇	semidirect
209. C₈×SD₁₆	C₂×C₁₃₇	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
#3396×C₁₃₇	2
#3394×C₁₃₇	2
#3342×C₁₃₇	2
#1706×C₁₃₇	2
#1674×C₁₃₇	2
#1667×C₁₃₇	2
#1666×C₁₃₇	2
#1640×C₁₃₇	2
#1628×C₁₃₇	2
C₈×Q₁₆×C₁₃₇	2
C₈×SD₁₆×C₁₃₇	2
#20018	137

Subgroups — C137×#20018 #46869404

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₇×#20018 #46869404